Junction Peak (4233m, 36.69150N / 118.3645W) is only 1km from Forester Pass (4017m), which is on
the John Muir trail, not far from Shepherd Pass (3672m).
It requires a long approach whichever way you come. Hence it is a strenuous
and long day hike.
The safest way is to climb it from Forester Pass.
If you are coming from Shepherd Pass, go straight west until you hit the John Muir trail (or take a short cut through Corner Lake) and turn right into this very popular trail. After moving relatively straight towards northeast, the trail will begin very steep switchbacks. Leave the trail where safe to do so and go right (east) and up towards the saddle between the peak to the east of Forester Pass and Junction Peak: Ski Mountaineer's Pass (not marked on most maps).
Ditto you are coming up from the northern side of Forester Pass (e.g. from Onion Valley): when you reach the pass, there will be this unnamed peak between you and Ski Mountaineer's Pass. You can either climb this peak (a waste of energy and time) or descend from Forester Pass on the trail briefly to the south until you find a point to start climbing around this peak to reach Ski Mountaineer's Pass.
When you are resting on this sandy saddle and enjoying the views of Mt Keith to the northeast, the west face of Junction Peak seems to have two horns but that's just an optical illusion: the one to the right is the real summit, whereas the thing to the left is just one of the many false summits.
There is one very broad chute that leads right to the summit, but it is way to the right. That is your intermediate destination. Where you start is a chute that ends pretty soon. You have to keep moving to the right as chutes dead-end against steep walls. Depending on how low you do this, you may have to cross 3 or 4 chutes before you reach the main chute. When you get to this broad chute, the summit is visible:
You should always be able to find a route that is class 3 or less, with little or no exposure, otherwise you waited too long to move to the next chute. When you get to the main chute, stay to the left to avoid the steep granite slabs and climb as far up as you can. When you hit the last wall, traverse to the right (which at this point is relatively safe) and head for a pyramidal rock. Circle counterclockwise around this rock and it should be obvious how to climb the summit block.
Distances (and 2014 time):
Southern ridge/faceThe most popular route, instead, is the southern route from Shepherd Pass via the Diamond Mesa (which in turn is best climbed by taking it at the southeast corner, northwest of Shepherd Pass). Read the page on Mt Williamson for details on how to get to the trailhead and the route up to Shepherd Pass.
The Diamond Mesa's north end is a sharp knife-edge ridge that leads to the southern summit. I would not recommend it unless you are equipped with ropes, helmets, etc. Also, the real summit is the farthest from Shepherd Pass of the many peaklets that dot Junction Peak.
An easier route from Shepherd Pass might be to head for the second major lake north of Shepherd Pass (3806m) and then climb the saddle between the real summit and the southern side of Junction Peak (the other peaks). From there one still has to climb a ridge with much exposure.
Note that Junction Peak has seven peaks, two of which compete for the real
summit: the true summit at the far northwestern end of the ridge.
Several pictures of Junction Peak viewed from Caltech Peak are here.
Distances (and 2012 time):
Pictures of this hike
Junction Peak from the south:
Junction Peak from the east:
The way from Forrester Pass:
(Forrester Pass is the black notch, the chute to Junction Peak is to the right of the peak immediately to the right of Forrester Pass)